Executive Summary
Preferred estimator: cross_section IV (Z4_90). Headline estimator selected from candidate instruments using IV first-stage strength (headline first-stage F=15.65). Headline outcome is gdp_pc_real_growth.
Trust Guide
- Trust most: diagnostics-backed estimator with strongest first-stage and transparent assumptions.
- Use RD sharp estimates as eligibility ITT unless funding first-stage is strong enough for fuzzy RD.
- Treat TWFE as benchmark sensitivity, not standalone causal proof.
Model Comparison
| estimator_family | model | outcome | window | term | coef | std_err | p_value | ci_95_lower | ci_95_upper | n_obs | n_regions | first_stage_f_stat | is_headline_estimator |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| IV (cross-section) | IV 2SLS cross-section (selected candidate) | gdp_pc_real_growth | post_2016_2020 | erdf_eur_pc_cum_2014_2020 | -0.003629 | 0.002129 | 0.088271 | -0.007803 | 0.000544 | 265 | 265 | 15.653611 | True |
| IV (panel) | IV 2SLS panel (selected candidate) | gdp_pc_real_growth | panel | erdf_eur_pc_l1 | -0.087141 | 0.095267 | 0.360351 | -0.273861 | 0.099580 | 1175 | 223 | 1.810335 | False |
| RD (sharp ITT) | Sharp RD bw=10.0 | gdp_pc_real_growth | post_2016_2020 | eligible_lt75 | -0.158809 | 1.375125 | 0.908059 | -2.854005 | 2.536387 | 53 | 53 | NaN | False |
| TWFE | Model A | gdp_pc_real_growth | panel | erdf_eur_pc_l1 | 0.005680 | 0.003025 | 0.060399 | -0.000248 | 0.011608 | 1175 | 223 | NaN | False |
| TWFE | Model B | gdp_pc_real_growth | panel | erdf_eur_pc_l1 | 0.003362 | 0.002888 | 0.244443 | -0.002299 | 0.009023 | 1175 | 223 | NaN | False |
| TWFE-dynamic | Model C (l1 term) | gdp_pc_real_growth | panel | erdf_eur_pc_l1 | 0.011999 | 0.004850 | 0.013356 | 0.002494 | 0.021505 | 861 | 223 | NaN | False |
Coverage by Year
Missingness Heatmap
Sample by Year
| year | n_rows | n_regions | headline_non_missing |
|---|---|---|---|
| 1986 | 398 | 398 | 0 |
| 1987 | 398 | 398 | 0 |
| 1988 | 398 | 398 | 0 |
| 1989 | 398 | 398 | 0 |
| 1990 | 398 | 398 | 0 |
| 1991 | 398 | 398 | 0 |
| 1992 | 398 | 398 | 0 |
| 1993 | 398 | 398 | 0 |
| 1994 | 398 | 398 | 0 |
| 1995 | 398 | 398 | 0 |
| 1996 | 398 | 398 | 0 |
| 1997 | 398 | 398 | 0 |
| 1998 | 398 | 398 | 0 |
| 1999 | 398 | 398 | 0 |
| 2000 | 398 | 398 | 0 |
| 2001 | 398 | 398 | 242 |
| 2002 | 398 | 398 | 242 |
| 2003 | 398 | 398 | 242 |
| 2004 | 398 | 398 | 242 |
| 2005 | 398 | 398 | 242 |
| 2006 | 398 | 398 | 242 |
| 2007 | 398 | 398 | 243 |
| 2008 | 398 | 398 | 243 |
| 2009 | 398 | 398 | 272 |
| 2010 | 398 | 398 | 272 |
| 2011 | 398 | 398 | 272 |
| 2012 | 398 | 398 | 272 |
| 2013 | 398 | 398 | 272 |
| 2014 | 398 | 398 | 272 |
| 2015 | 398 | 398 | 272 |
| 2016 | 398 | 398 | 272 |
| 2017 | 398 | 398 | 272 |
| 2018 | 398 | 398 | 272 |
| 2019 | 398 | 398 | 272 |
| 2020 | 398 | 398 | 272 |
| 2021 | 398 | 398 | 272 |
| 2022 | 398 | 398 | 269 |
| 2023 | 398 | 398 | 269 |
| 2024 | 398 | 398 | 0 |
| 2025 | 398 | 398 | 0 |
Sample by Country
| country | n_regions | n_rows | headline_non_missing |
|---|---|---|---|
| FR | 52 | 2080 | 621 |
| UK | 45 | 1800 | 0 |
| DE | 38 | 1520 | 874 |
| TR | 26 | 1040 | 390 |
| PL | 23 | 920 | 391 |
| EL | 22 | 880 | 299 |
| IT | 21 | 840 | 483 |
| ES | 19 | 760 | 437 |
| NL | 14 | 560 | 230 |
| PT | 12 | 480 | 92 |
| NO | 11 | 440 | 0 |
| BE | 11 | 440 | 253 |
| HU | 9 | 360 | 184 |
| AT | 9 | 360 | 207 |
| CZ | 8 | 320 | 184 |
| RO | 8 | 320 | 184 |
| SE | 8 | 320 | 184 |
| CH | 7 | 280 | 0 |
| BG | 6 | 240 | 138 |
| DK | 5 | 200 | 115 |
| FI | 5 | 200 | 115 |
| HR | 5 | 200 | 92 |
| IE | 5 | 200 | 69 |
| SI | 4 | 160 | 46 |
| SK | 4 | 160 | 92 |
| RS | 4 | 160 | 92 |
| AL | 3 | 120 | 39 |
| LT | 3 | 120 | 46 |
| MT | 1 | 40 | 23 |
| MK | 1 | 40 | 23 |
| ME | 1 | 40 | 17 |
| LV | 1 | 40 | 23 |
| LU | 1 | 40 | 23 |
| LI | 1 | 40 | 0 |
| EU | 1 | 40 | 0 |
| EF | 1 | 40 | 0 |
| EE | 1 | 40 | 23 |
| CY | 1 | 40 | 23 |
| IS | 1 | 40 | 0 |
Overview Table
| metric | value |
|---|---|
| min_year | 1986 |
| max_year | 2025 |
| n_regions | 398 |
| n_rows | 15920 |
| headline_outcome | gdp_pc_real_growth |
Key Variable Definitions
Running variable: r = GDPpc_PPS / EU average × 100 (reference years 2007-2009; fallback <=2013).
Eligibility: eligible_lt75 = 1[r < 75], eligible_lt90 = 1[r < 90].
Exposure: erdf_eur_pc_l1 and cumulative erdf_eur_pc_cum_2014_2020.
Headline outcome: gdp_pc_real_growth.
Specification
Model A: outcome ~ erdf_l1 + controls + region FE + year FE
Model B: outcome ~ erdf_l1 + controls + region FE + country×year FE
Model C: outcome ~ erdf_l1 + erdf_l2 + erdf_l3 + controls + region FE + year FE
Dynamic Lag Plot
TWFE Main
| outcome | model | term | coef | std_err | t_stat | p_value | ci_95_lower | ci_95_upper | n_obs | n_regions | fe_type | clustering | sample_year_min | sample_year_max | controls_used |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| gdp_pc_real_growth | Model A | erdf_eur_pc_l1 | 0.005680 | 0.003025 | 1.877873 | 6.039856e-02 | -0.000248 | 0.011608 | 1175 | 223 | year | nuts2 | 2017 | 2023 | unemp_rate,emp_rate,tertiary_share_25_64,rd_gerd,gva |
| gdp_pc_real_growth | Model A | unemp_rate | -0.645481 | 0.083054 | -7.771818 | 7.736728e-15 | -0.808264 | -0.482698 | 1175 | 223 | year | nuts2 | 2017 | 2023 | unemp_rate,emp_rate,tertiary_share_25_64,rd_gerd,gva |
| gdp_pc_real_growth | Model A | emp_rate | -0.311572 | 0.097518 | -3.195020 | 1.398212e-03 | -0.502704 | -0.120440 | 1175 | 223 | year | nuts2 | 2017 | 2023 | unemp_rate,emp_rate,tertiary_share_25_64,rd_gerd,gva |
| gdp_pc_real_growth | Model A | tertiary_share_25_64 | -0.196250 | 0.092246 | -2.127452 | 3.338256e-02 | -0.377049 | -0.015450 | 1175 | 223 | year | nuts2 | 2017 | 2023 | unemp_rate,emp_rate,tertiary_share_25_64,rd_gerd,gva |
| gdp_pc_real_growth | Model A | rd_gerd | -0.780868 | 0.538157 | -1.451004 | 1.467787e-01 | -1.835636 | 0.273900 | 1175 | 223 | year | nuts2 | 2017 | 2023 | unemp_rate,emp_rate,tertiary_share_25_64,rd_gerd,gva |
| gdp_pc_real_growth | Model A | gva | 0.143671 | 0.035563 | 4.039922 | 5.346901e-05 | 0.073969 | 0.213374 | 1175 | 223 | year | nuts2 | 2017 | 2023 | unemp_rate,emp_rate,tertiary_share_25_64,rd_gerd,gva |
| gdp_pc_real_growth | Model B | erdf_eur_pc_l1 | 0.003362 | 0.002888 | 1.163952 | 2.444433e-01 | -0.002299 | 0.009023 | 1175 | 223 | country_year | nuts2 | 2017 | 2023 | unemp_rate,emp_rate,tertiary_share_25_64,rd_gerd,gva |
| gdp_pc_real_growth | Model B | unemp_rate | 0.010578 | 0.104282 | 0.101436 | 9.192041e-01 | -0.193811 | 0.214967 | 1175 | 223 | country_year | nuts2 | 2017 | 2023 | unemp_rate,emp_rate,tertiary_share_25_64,rd_gerd,gva |
| gdp_pc_real_growth | Model B | emp_rate | -0.040660 | 0.123919 | -0.328117 | 7.428229e-01 | -0.283536 | 0.202217 | 1175 | 223 | country_year | nuts2 | 2017 | 2023 | unemp_rate,emp_rate,tertiary_share_25_64,rd_gerd,gva |
| gdp_pc_real_growth | Model B | tertiary_share_25_64 | -0.101720 | 0.101736 | -0.999845 | 3.173854e-01 | -0.301119 | 0.097679 | 1175 | 223 | country_year | nuts2 | 2017 | 2023 | unemp_rate,emp_rate,tertiary_share_25_64,rd_gerd,gva |
| gdp_pc_real_growth | Model B | rd_gerd | -0.539994 | 0.601826 | -0.897260 | 3.695802e-01 | -1.719551 | 0.639563 | 1175 | 223 | country_year | nuts2 | 2017 | 2023 | unemp_rate,emp_rate,tertiary_share_25_64,rd_gerd,gva |
| gdp_pc_real_growth | Model B | gva | 0.220716 | 0.065134 | 3.388648 | 7.023807e-04 | 0.093056 | 0.348377 | 1175 | 223 | country_year | nuts2 | 2017 | 2023 | unemp_rate,emp_rate,tertiary_share_25_64,rd_gerd,gva |
Distributed Lags
| outcome | model | term | coef | std_err | t_stat | p_value | ci_95_lower | ci_95_upper | n_obs | n_regions | fe_type | clustering | sample_year_min | sample_year_max | controls_used |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| gdp_pc_real_growth | Model C | erdf_eur_pc_l1 | 0.011999 | 0.004850 | 2.474144 | 0.013356 | 0.002494 | 0.021505 | 861 | 223 | year | nuts2 | 2019 | 2023 | unemp_rate,emp_rate,tertiary_share_25_64,rd_gerd,gva |
| gdp_pc_real_growth | Model C | erdf_eur_pc_l2 | 0.007897 | 0.003778 | 2.089908 | 0.036626 | 0.000491 | 0.015302 | 861 | 223 | year | nuts2 | 2019 | 2023 | unemp_rate,emp_rate,tertiary_share_25_64,rd_gerd,gva |
| gdp_pc_real_growth | Model C | erdf_eur_pc_l3 | -0.003085 | 0.002665 | -1.157747 | 0.246967 | -0.008309 | 0.002138 | 861 | 223 | year | nuts2 | 2019 | 2023 | unemp_rate,emp_rate,tertiary_share_25_64,rd_gerd,gva |
| gdp_pc_real_growth | Model C | unemp_rate | -0.623873 | 0.152467 | -4.091862 | 0.000043 | -0.922702 | -0.325044 | 861 | 223 | year | nuts2 | 2019 | 2023 | unemp_rate,emp_rate,tertiary_share_25_64,rd_gerd,gva |
| gdp_pc_real_growth | Model C | emp_rate | -0.276854 | 0.121080 | -2.286541 | 0.022223 | -0.514166 | -0.039542 | 861 | 223 | year | nuts2 | 2019 | 2023 | unemp_rate,emp_rate,tertiary_share_25_64,rd_gerd,gva |
| gdp_pc_real_growth | Model C | tertiary_share_25_64 | -0.297705 | 0.129373 | -2.301129 | 0.021384 | -0.551272 | -0.044138 | 861 | 223 | year | nuts2 | 2019 | 2023 | unemp_rate,emp_rate,tertiary_share_25_64,rd_gerd,gva |
| gdp_pc_real_growth | Model C | rd_gerd | -1.427459 | 0.723457 | -1.973108 | 0.048483 | -2.845409 | -0.009509 | 861 | 223 | year | nuts2 | 2019 | 2023 | unemp_rate,emp_rate,tertiary_share_25_64,rd_gerd,gva |
| gdp_pc_real_growth | Model C | gva | 0.207709 | 0.051100 | 4.064715 | 0.000048 | 0.107554 | 0.307864 | 861 | 223 | year | nuts2 | 2019 | 2023 | unemp_rate,emp_rate,tertiary_share_25_64,rd_gerd,gva |
Funding Discontinuity (First Stage)
Outcome RD Sensitivity
Funding Jump Table
| bandwidth | jump_coef | std_err | t_stat | p_value | ci_95_lower | ci_95_upper | n_obs | n_left | n_right | first_stage_f_stat | jump_over_sd | fuzzy_rd_viable | viability_reason |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 5.0 | 605.065522 | 582.900134 | 1.038026 | 0.299258 | -537.397747 | 1747.528790 | 23 | 11 | 12 | 1.077498 | 2.372630 | False | funding jump imprecise/weak (first-stage F below 10) |
| 7.5 | 628.143677 | 482.715678 | 1.301271 | 0.193166 | -317.961667 | 1574.249020 | 41 | 18 | 23 | 1.693305 | 2.463126 | False | funding jump imprecise/weak (first-stage F below 10) |
| 10.0 | 521.675581 | 405.834631 | 1.285439 | 0.198639 | -273.745679 | 1317.096842 | 53 | 24 | 29 | 1.652353 | 2.045635 | False | funding jump imprecise/weak (first-stage F below 10) |
| 12.5 | 406.564050 | 356.718003 | 1.139735 | 0.254397 | -292.590388 | 1105.718489 | 65 | 26 | 39 | 1.298996 | 1.594251 | False | funding jump imprecise/weak (first-stage F below 10) |
| 15.0 | 323.631425 | 308.232033 | 1.049960 | 0.293736 | -280.492259 | 927.755109 | 78 | 32 | 46 | 1.102417 | 1.269049 | False | funding jump imprecise/weak (first-stage F below 10) |
| 20.0 | 277.562241 | 251.486822 | 1.103685 | 0.269730 | -215.342872 | 770.467353 | 95 | 39 | 56 | 1.218121 | 1.088399 | False | funding jump imprecise/weak (first-stage F below 10) |
Sharp RD Outcomes
| outcome | window | bandwidth | coef | std_err | t_stat | p_value | ci_95_lower | ci_95_upper | n_obs | n_left | n_right | interpretation |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| gdp_pc_pps_growth | post_2016_2020 | 10.0 | -1.970790 | 1.536487 | -1.282659 | 0.199611 | -4.982249 | 1.040670 | 53 | 24 | 29 | eligibility ITT effect (sharp RD at 75 cutoff) |
| gdp_pc_pps_growth | post_2021_2023 | 10.0 | 2.840440 | 1.201786 | 2.363516 | 0.018102 | 0.484983 | 5.195897 | 53 | 24 | 29 | eligibility ITT effect (sharp RD at 75 cutoff) |
| gdp_pc_real_growth | post_2016_2020 | 10.0 | -0.158809 | 1.375125 | -0.115487 | 0.908059 | -2.854005 | 2.536387 | 53 | 24 | 29 | eligibility ITT effect (sharp RD at 75 cutoff) |
| gdp_pc_real_growth | post_2021_2023 | 10.0 | 2.420227 | 0.975072 | 2.482100 | 0.013061 | 0.509120 | 4.331333 | 53 | 24 | 29 | eligibility ITT effect (sharp RD at 75 cutoff) |
Placebo Pretrend
| outcome | window | bandwidth | coef | std_err | t_stat | p_value | ci_95_lower | ci_95_upper | n_obs | n_left | n_right | interpretation |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| gdp_pc_real_growth | pre_2010_2013 | 10.0 | -1.941947 | 2.455542 | -0.790842 | 0.429036 | -6.754721 | 2.870828 | 53 | 24 | 29 | placebo pretrend jump should be near zero |


Instrument Candidate Leaderboard
| candidate_id | candidate_label | sample_type | spec_name | endogenous_var | instrument_var | fe_spec | controls_used | n_obs | n_regions | coef | std_err | t_stat | p_value | f_stat | partial_r2 | status | status_reason | iv_first_stage_f_headline |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Z1 | eligible_lt75 × post2014 | panel | region_FE + year_FE | erdf_eur_pc_l1 | z1_post75 | C(nuts2_id) + C(year) | unemp_rate,emp_rate,tertiary_share_25_64,rd_gerd,gva | 1175 | 223 | NaN | NaN | NaN | NaN | NaN | NaN | failed | instrument has no within-nuts2_id variation under FE | NaN |
| Z4_75 | eligible_lt75 (cross-section cumulative exposure) | cross_section | country_FE + pre_controls | erdf_eur_pc_cum_2014_2020 | eligible_lt75 | C(country) | log_gdp_pc_real_pre_2010_2013,unemp_rate_pre_2010_2013,emp_rate_pre_2010_2013 | 264 | 264 | 164.946046 | 50.403745 | 3.272496 | 0.001231 | 10.709229 | 0.044676 | ok | 4.599386 | |
| Z4_75 | eligible_lt75 (cross-section cumulative exposure) | cross_section | country_FE + pre_controls | erdf_eur_pc_cum_2015_2020 | eligible_lt75 | C(country) | log_gdp_pc_real_pre_2010_2013,unemp_rate_pre_2010_2013,emp_rate_pre_2010_2013 | 264 | 264 | 164.946046 | 50.403745 | 3.272496 | 0.001231 | 10.709229 | 0.044676 | ok | 4.599386 | |
| Z4_90 | eligible_lt90 (cross-section cumulative exposure) | cross_section | country_FE + pre_controls | erdf_eur_pc_cum_2014_2020 | eligible_lt90 | C(country) | log_gdp_pc_real_pre_2010_2013,unemp_rate_pre_2010_2013,emp_rate_pre_2010_2013 | 265 | 265 | 123.463932 | 39.825603 | 3.100115 | 0.002176 | 9.610710 | 0.040110 | ok | 15.653611 | |
| Z4_90 | eligible_lt90 (cross-section cumulative exposure) | cross_section | country_FE + pre_controls | erdf_eur_pc_cum_2015_2020 | eligible_lt90 | C(country) | log_gdp_pc_real_pre_2010_2013,unemp_rate_pre_2010_2013,emp_rate_pre_2010_2013 | 265 | 265 | 123.463932 | 39.825603 | 3.100115 | 0.002176 | 9.610710 | 0.040110 | ok | 15.653611 | |
| Z5 | eligible_lt90 × eu_mean_erdf_t | panel | region_FE + year_FE | erdf_eur_pc_l1 | z5_eu90 | C(nuts2_id) + C(year) | unemp_rate,emp_rate,tertiary_share_25_64,rd_gerd,gva | 1175 | 223 | 0.144886 | 0.120613 | 1.201250 | 0.229654 | 1.443002 | 0.001610 | ok | NaN | |
| Z2 | eligible_lt75 × eu_mean_erdf_t | panel | region_FE + year_FE | erdf_eur_pc_l1 | z2_eu75 | C(nuts2_id) + C(year) | unemp_rate,emp_rate,tertiary_share_25_64,rd_gerd,gva | 1175 | 223 | 0.163688 | 0.147836 | 1.107222 | 0.268198 | 1.225941 | 0.001804 | ok | NaN | |
| Z3 | eligible_lt75 × country_mean_erdf_t_loo | panel | region_FE + year_FE | erdf_eur_pc_l1 | z3_country75 | C(nuts2_id) + C(year) | unemp_rate,emp_rate,tertiary_share_25_64,rd_gerd,gva | 1131 | 216 | -0.060115 | 0.056913 | -1.056254 | 0.290852 | 1.115672 | 0.001873 | ok | NaN |
First-stage Scatter
Panel IV Results
| outcome | model | sample_type | term | instrument | coef | std_err | t_stat | p_value | ci_95_lower | ci_95_upper | first_stage_f_stat | n_obs | n_regions | sample_year_min | sample_year_max | controls_used | fe_spec |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| gdp_pc_real_growth | IV 2SLS panel (selected candidate) | panel | erdf_eur_pc_l1 | z5_eu90 | -0.087141 | 0.095267 | -0.914697 | 0.360351 | -0.273861 | 0.09958 | 1.810335 | 1175 | 223 | 2017 | 2023 | unemp_rate,emp_rate,tertiary_share_25_64,rd_gerd,gva | region_FE + year_FE |
Cross-section IV Results
| outcome | window | model | sample_type | term | instrument | coef | std_err | t_stat | p_value | ci_95_lower | ci_95_upper | first_stage_f_stat | n_obs | n_regions | controls_used | fe_spec |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| gdp_pc_real_growth | post_2016_2020 | IV 2SLS cross-section (selected candidate) | cross_section | erdf_eur_pc_cum_2014_2020 | eligible_lt90 | -0.003629 | 0.002129 | -1.704590 | 0.088271 | -0.007803 | 0.000544 | 15.653611 | 265 | 265 | log_gdp_pc_real_pre_2010_2013,unemp_rate_pre_2010_2013,emp_rate_pre_2010_2013 | country_FE |
| gdp_pc_real_growth | post_2021_2023 | IV 2SLS cross-section (selected candidate) | cross_section | erdf_eur_pc_cum_2014_2020 | eligible_lt90 | -0.005085 | 0.002798 | -1.817175 | 0.069190 | -0.010570 | 0.000400 | 15.653611 | 265 | 265 | log_gdp_pc_real_pre_2010_2013,unemp_rate_pre_2010_2013,emp_rate_pre_2010_2013 | country_FE |
| gdp_pc_pps_growth | post_2016_2020 | IV 2SLS cross-section (selected candidate) | cross_section | erdf_eur_pc_cum_2014_2020 | eligible_lt90 | -0.002467 | 0.001670 | -1.477074 | 0.139656 | -0.005741 | 0.000807 | 15.653611 | 265 | 265 | log_gdp_pc_real_pre_2010_2013,unemp_rate_pre_2010_2013,emp_rate_pre_2010_2013 | country_FE |
| gdp_pc_pps_growth | post_2021_2023 | IV 2SLS cross-section (selected candidate) | cross_section | erdf_eur_pc_cum_2014_2020 | eligible_lt90 | -0.000998 | 0.002209 | -0.452017 | 0.651256 | -0.005327 | 0.003330 | 15.653611 | 265 | 265 | log_gdp_pc_real_pre_2010_2013,unemp_rate_pre_2010_2013,emp_rate_pre_2010_2013 | country_FE |
Robustness Table
| outcome | model | term | coef | std_err | t_stat | p_value | ci_95_lower | ci_95_upper | n_obs | n_regions | fe_type | clustering | sample_year_min | sample_year_max | controls_used | outlier_rule | erdf_eur_pc_global_p99 | balanced_window_start | balanced_window_end | balanced_regions | treatment_scale |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| gdp_pc_real_growth | Model A (outliers excluded) | erdf_eur_pc_l1 | 0.006324 | 0.003033 | 2.084936 | 0.037075 | 0.000379 | 0.012268 | 1156 | 223 | year | nuts2 | 2017 | 2023 | unemp_rate,emp_rate,tertiary_share_25_64,rd_gerd,gva | drop global top 1% erdf_eur_pc | 264.108343 | NaN | NaN | NaN | NaN |
| gdp_pc_real_growth | Model B (outliers excluded) | erdf_eur_pc_l1 | 0.003256 | 0.002984 | 1.091103 | 0.275227 | -0.002593 | 0.009104 | 1156 | 223 | country_year | nuts2 | 2017 | 2023 | unemp_rate,emp_rate,tertiary_share_25_64,rd_gerd,gva | drop global top 1% erdf_eur_pc | 264.108343 | NaN | NaN | NaN | NaN |
| gdp_pc_real_growth | Model A (balanced panel) | erdf_eur_pc_l1 | 0.005542 | 0.003063 | 1.809299 | 0.070405 | -0.000462 | 0.011546 | 805 | 115 | year | nuts2 | 2017 | 2023 | unemp_rate,emp_rate,tertiary_share_25_64,rd_gerd,gva | NaN | NaN | 2017.0 | 2023.0 | 115.0 | NaN |
| gdp_pc_real_growth | Model B (balanced panel) | erdf_eur_pc_l1 | 0.002715 | 0.003029 | 0.896323 | 0.370080 | -0.003222 | 0.008652 | 805 | 115 | country_year | nuts2 | 2017 | 2023 | unemp_rate,emp_rate,tertiary_share_25_64,rd_gerd,gva | NaN | NaN | 2017.0 | 2023.0 | 115.0 | NaN |
| gdp_pc_real_growth | Model A (scaled treatment) | erdf_k_eur_pc_l1 | 5.679637 | 3.024506 | 1.877873 | 0.060399 | -0.248285 | 11.607559 | 1175 | 223 | year | nuts2 | 2017 | 2023 | unemp_rate,emp_rate,tertiary_share_25_64,rd_gerd,gva | NaN | NaN | NaN | NaN | NaN | EUR 1,000 per capita |
| gdp_pc_real_growth | Model B (scaled treatment) | erdf_k_eur_pc_l1 | 3.361760 | 2.888228 | 1.163952 | 0.244443 | -2.299063 | 9.022584 | 1175 | 223 | country_year | nuts2 | 2017 | 2023 | unemp_rate,emp_rate,tertiary_share_25_64,rd_gerd,gva | NaN | NaN | NaN | NaN | NaN | EUR 1,000 per capita |
Outcome Robustness (Real vs PPS)
| outcome | model | coef | std_err | p_value | n_obs | n_regions |
|---|---|---|---|---|---|---|
| gdp_pc_real_growth | Model A | 0.005680 | 0.003025 | 0.060399 | 1175 | 223 |
| gdp_pc_real_growth | Model B | 0.003362 | 0.002888 | 0.244443 | 1175 | 223 |
| gdp_pc_pps_growth | Model A | 0.002522 | 0.003617 | 0.485532 | 1175 | 223 |
| gdp_pc_pps_growth | Model B | 0.001134 | 0.002851 | 0.690810 | 1175 | 223 |
| gdp_pc_growth | Model A | 0.002075 | 0.003657 | 0.570518 | 1175 | 223 |
| gdp_pc_growth | Model B | 0.003646 | 0.004183 | 0.383407 | 1175 | 223 |
Sigma Convergence
Beta Convergence
| outcome | model | term | coef | std_err | t_stat | p_value | ci_95_lower | ci_95_upper | n_obs | n_regions | fe_type | clustering | sample_year_min | sample_year_max | controls_used |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| gdp_pc_real_growth | Model D | log_gdp_pc_real_l1 | -5.267283 | 0.602008 | -8.749527 | 2.142487e-18 | -6.447197 | -4.087370 | 6012 | 272 | year | nuts2 | 2001 | 2023 | |
| gdp_pc_real_growth | Model E | log_gdp_pc_real_l1 | -103.618010 | 1.785512 | -58.032653 | 0.000000e+00 | -107.117550 | -100.118470 | 1175 | 223 | year | nuts2 | 2017 | 2023 | unemp_rate,emp_rate,tertiary_share_25_64,rd_gerd,gva |
| gdp_pc_real_growth | Model E | erdf_eur_pc_l1 | -0.010347 | 0.019129 | -0.540894 | 5.885808e-01 | -0.047840 | 0.027146 | 1175 | 223 | year | nuts2 | 2017 | 2023 | unemp_rate,emp_rate,tertiary_share_25_64,rd_gerd,gva |
| gdp_pc_real_growth | Model E | erdf_eur_pc_l1:log_gdp_pc_real_l1 | 0.001197 | 0.002027 | 0.590463 | 5.548802e-01 | -0.002776 | 0.005169 | 1175 | 223 | year | nuts2 | 2017 | 2023 | unemp_rate,emp_rate,tertiary_share_25_64,rd_gerd,gva |
| gdp_pc_real_growth | Model E | unemp_rate | -0.070479 | 0.061746 | -1.141445 | 2.536847e-01 | -0.191499 | 0.050540 | 1175 | 223 | year | nuts2 | 2017 | 2023 | unemp_rate,emp_rate,tertiary_share_25_64,rd_gerd,gva |
| gdp_pc_real_growth | Model E | emp_rate | 0.035694 | 0.042576 | 0.838360 | 4.018284e-01 | -0.047754 | 0.119142 | 1175 | 223 | year | nuts2 | 2017 | 2023 | unemp_rate,emp_rate,tertiary_share_25_64,rd_gerd,gva |
| gdp_pc_real_growth | Model E | tertiary_share_25_64 | -0.025351 | 0.029103 | -0.871060 | 3.837213e-01 | -0.082392 | 0.031691 | 1175 | 223 | year | nuts2 | 2017 | 2023 | unemp_rate,emp_rate,tertiary_share_25_64,rd_gerd,gva |
| gdp_pc_real_growth | Model E | rd_gerd | 0.233428 | 0.200718 | 1.162964 | 2.448443e-01 | -0.159972 | 0.626828 | 1175 | 223 | year | nuts2 | 2017 | 2023 | unemp_rate,emp_rate,tertiary_share_25_64,rd_gerd,gva |
| gdp_pc_real_growth | Model E | gva | 0.819057 | 0.026602 | 30.788784 | 3.702864e-208 | 0.766917 | 0.871197 | 1175 | 223 | year | nuts2 | 2017 | 2023 | unemp_rate,emp_rate,tertiary_share_25_64,rd_gerd,gva |
| gdp_pc_real_growth | Model E (country-year FE) | log_gdp_pc_real_l1 | -101.340054 | 2.976162 | -34.050586 | 3.978591e-254 | -107.173224 | -95.506884 | 1175 | 223 | country_year | nuts2 | 2017 | 2023 | unemp_rate,emp_rate,tertiary_share_25_64,rd_gerd,gva |
| gdp_pc_real_growth | Model E (country-year FE) | erdf_eur_pc_l1 | 0.030058 | 0.025919 | 1.159668 | 2.461839e-01 | -0.020743 | 0.080859 | 1175 | 223 | country_year | nuts2 | 2017 | 2023 | unemp_rate,emp_rate,tertiary_share_25_64,rd_gerd,gva |
| gdp_pc_real_growth | Model E (country-year FE) | erdf_eur_pc_l1:log_gdp_pc_real_l1 | -0.003032 | 0.002648 | -1.145086 | 2.521736e-01 | -0.008222 | 0.002158 | 1175 | 223 | country_year | nuts2 | 2017 | 2023 | unemp_rate,emp_rate,tertiary_share_25_64,rd_gerd,gva |
| gdp_pc_real_growth | Model E (country-year FE) | unemp_rate | 0.038362 | 0.076465 | 0.501698 | 6.158801e-01 | -0.111506 | 0.188230 | 1175 | 223 | country_year | nuts2 | 2017 | 2023 | unemp_rate,emp_rate,tertiary_share_25_64,rd_gerd,gva |
| gdp_pc_real_growth | Model E (country-year FE) | emp_rate | 0.058033 | 0.059142 | 0.981258 | 3.264655e-01 | -0.057882 | 0.173949 | 1175 | 223 | country_year | nuts2 | 2017 | 2023 | unemp_rate,emp_rate,tertiary_share_25_64,rd_gerd,gva |
| gdp_pc_real_growth | Model E (country-year FE) | tertiary_share_25_64 | -0.038208 | 0.022010 | -1.735898 | 8.258192e-02 | -0.081347 | 0.004932 | 1175 | 223 | country_year | nuts2 | 2017 | 2023 | unemp_rate,emp_rate,tertiary_share_25_64,rd_gerd,gva |
| gdp_pc_real_growth | Model E (country-year FE) | rd_gerd | 0.131189 | 0.188324 | 0.696612 | 4.860457e-01 | -0.237919 | 0.500296 | 1175 | 223 | country_year | nuts2 | 2017 | 2023 | unemp_rate,emp_rate,tertiary_share_25_64,rd_gerd,gva |
| gdp_pc_real_growth | Model E (country-year FE) | gva | 0.832225 | 0.037628 | 22.117185 | 2.159915e-108 | 0.758476 | 0.905975 | 1175 | 223 | country_year | nuts2 | 2017 | 2023 | unemp_rate,emp_rate,tertiary_share_25_64,rd_gerd,gva |
| gdp_pc_pps_growth | Model D | log_gdp_pc_pps_l1 | -7.724735 | 0.435866 | -17.722744 | 2.799174e-70 | -8.579015 | -6.870454 | 6218 | 292 | year | nuts2 | 2001 | 2023 | |
| gdp_pc_pps_growth | Model E | log_gdp_pc_pps_l1 | -52.178507 | 6.741167 | -7.740278 | 9.919962e-15 | -65.390952 | -38.966063 | 1175 | 223 | year | nuts2 | 2017 | 2023 | unemp_rate,emp_rate,tertiary_share_25_64,rd_gerd,gva |
| gdp_pc_pps_growth | Model E | erdf_eur_pc_l1 | -0.015846 | 0.088078 | -0.179914 | 8.572202e-01 | -0.188476 | 0.156783 | 1175 | 223 | year | nuts2 | 2017 | 2023 | unemp_rate,emp_rate,tertiary_share_25_64,rd_gerd,gva |
| gdp_pc_pps_growth | Model E | erdf_eur_pc_l1:log_gdp_pc_pps_l1 | 0.001914 | 0.008857 | 0.216114 | 8.288986e-01 | -0.015446 | 0.019274 | 1175 | 223 | year | nuts2 | 2017 | 2023 | unemp_rate,emp_rate,tertiary_share_25_64,rd_gerd,gva |
| gdp_pc_pps_growth | Model E | unemp_rate | -0.371136 | 0.086686 | -4.281399 | 1.857220e-05 | -0.541036 | -0.201235 | 1175 | 223 | year | nuts2 | 2017 | 2023 | unemp_rate,emp_rate,tertiary_share_25_64,rd_gerd,gva |
| gdp_pc_pps_growth | Model E | emp_rate | -0.031546 | 0.128419 | -0.245651 | 8.059522e-01 | -0.283242 | 0.220150 | 1175 | 223 | year | nuts2 | 2017 | 2023 | unemp_rate,emp_rate,tertiary_share_25_64,rd_gerd,gva |
| gdp_pc_pps_growth | Model E | tertiary_share_25_64 | -0.406706 | 0.094194 | -4.317739 | 1.576355e-05 | -0.591323 | -0.222088 | 1175 | 223 | year | nuts2 | 2017 | 2023 | unemp_rate,emp_rate,tertiary_share_25_64,rd_gerd,gva |
| gdp_pc_pps_growth | Model E | rd_gerd | -1.072647 | 0.617415 | -1.737319 | 8.233096e-02 | -2.282759 | 0.137465 | 1175 | 223 | year | nuts2 | 2017 | 2023 | unemp_rate,emp_rate,tertiary_share_25_64,rd_gerd,gva |
| gdp_pc_pps_growth | Model E | gva | 0.371331 | 0.066120 | 5.615996 | 1.954328e-08 | 0.241738 | 0.500924 | 1175 | 223 | year | nuts2 | 2017 | 2023 | unemp_rate,emp_rate,tertiary_share_25_64,rd_gerd,gva |
| gdp_pc_pps_growth | Model E (country-year FE) | log_gdp_pc_pps_l1 | -56.803175 | 5.619697 | -10.107871 | 5.097999e-24 | -67.817579 | -45.788771 | 1175 | 223 | country_year | nuts2 | 2017 | 2023 | unemp_rate,emp_rate,tertiary_share_25_64,rd_gerd,gva |
| gdp_pc_pps_growth | Model E (country-year FE) | erdf_eur_pc_l1 | -0.018215 | 0.062550 | -0.291207 | 7.708930e-01 | -0.140811 | 0.104381 | 1175 | 223 | country_year | nuts2 | 2017 | 2023 | unemp_rate,emp_rate,tertiary_share_25_64,rd_gerd,gva |
| gdp_pc_pps_growth | Model E (country-year FE) | erdf_eur_pc_l1:log_gdp_pc_pps_l1 | 0.001788 | 0.006265 | 0.285369 | 7.753618e-01 | -0.010491 | 0.014067 | 1175 | 223 | country_year | nuts2 | 2017 | 2023 | unemp_rate,emp_rate,tertiary_share_25_64,rd_gerd,gva |
| gdp_pc_pps_growth | Model E (country-year FE) | unemp_rate | -0.046387 | 0.109807 | -0.422438 | 6.727057e-01 | -0.261605 | 0.168832 | 1175 | 223 | country_year | nuts2 | 2017 | 2023 | unemp_rate,emp_rate,tertiary_share_25_64,rd_gerd,gva |
| gdp_pc_pps_growth | Model E (country-year FE) | emp_rate | 0.100771 | 0.128720 | 0.782876 | 4.336999e-01 | -0.151514 | 0.353057 | 1175 | 223 | country_year | nuts2 | 2017 | 2023 | unemp_rate,emp_rate,tertiary_share_25_64,rd_gerd,gva |
| gdp_pc_pps_growth | Model E (country-year FE) | tertiary_share_25_64 | -0.186769 | 0.075992 | -2.457730 | 1.398184e-02 | -0.335711 | -0.037826 | 1175 | 223 | country_year | nuts2 | 2017 | 2023 | unemp_rate,emp_rate,tertiary_share_25_64,rd_gerd,gva |
| gdp_pc_pps_growth | Model E (country-year FE) | rd_gerd | -0.830514 | 0.577538 | -1.438025 | 1.504269e-01 | -1.962467 | 0.301439 | 1175 | 223 | country_year | nuts2 | 2017 | 2023 | unemp_rate,emp_rate,tertiary_share_25_64,rd_gerd,gva |
| gdp_pc_pps_growth | Model E (country-year FE) | gva | 0.273376 | 0.069326 | 3.943330 | 8.035797e-05 | 0.137499 | 0.409252 | 1175 | 223 | country_year | nuts2 | 2017 | 2023 | unemp_rate,emp_rate,tertiary_share_25_64,rd_gerd,gva |
Limitations
- Real GDP per capita is reconstructed from volume indices, not direct chain-linked real EUR levels.
- Eligibility and running-variable coverage is partial because of NUTS coverage differences.
- Interpret RD as eligibility ITT unless funding first-stage is strong.
- Interpret IV as causal only when first-stage diagnostics are strong and stable.
Interpretation Guardrails
Supported claims
Associations and policy-rule-based estimates under the maintained exclusion assumptions and observed first-stage strength diagnostics.
Unsupported claims
Universal structural treatment effects across all regions/times, especially when first-stage strength falls below conventional thresholds.
Next steps
Strengthen external instrument design (national envelopes/programmatic shocks), harmonize category coverage under NUTS revisions, and test alternative deflators/PPS-based real outcomes.